login
Primes p such that x^30 = 2 has no solution mod p.
2

%I #9 Sep 08 2022 08:45:02

%S 3,5,7,11,13,19,29,31,37,41,43,53,59,61,67,71,73,79,83,97,101,103,107,

%T 109,131,139,149,151,157,163,173,179,181,191,193,197,199,211,227,229,

%U 241,251,269,271,277,281,283,293,307,311,313,317,331,337,347,349,367

%N Primes p such that x^30 = 2 has no solution mod p.

%C Complement of A049562 relative to A000040.

%H Vincenzo Librandi, <a href="/A059334/b059334.txt">Table of n, a(n) for n = 1..1000</a>

%t ok[p_] := Reduce[Mod[x^30 - 2, p] == 0, x, Integers] == False; Select[Prime[Range[80]], ok ] (* _Vincenzo Librandi_, Sep 20 2012 *)

%o (Magma) [p: p in PrimesUpTo(400) | not exists{x : x in ResidueClassRing(p) | x^30 eq 2} ]; // _Vincenzo Librandi_, Sep 20 2012

%Y A000040, A049562.

%K nonn,easy

%O 1,1

%A _Klaus Brockhaus_, Jan 26 2001